This paper is a follow-up to [J. High Energy Phys. 06, 025 (2020)] in which two-dimensional
conformal field theories in the presence of spin structures are studied. In the present paper …

We describe partial semi-simplicial resolutions of moduli spaces of surfaces with tangential
structure. This allows us to prove a homological stability theorem for these moduli spaces …

We provide a mathematical proposal for the anomaly indicators of symmetries of (2+ 1)-d
fermionic topological orders, and work out the consequences of our proposal in several …

This paper derives a large web of exact lattice dualities in one and two spatial dimensions.
Some of the dualities are well-known, while others, such as two-dimensional boson …

This paper investigates the relationship between strata of abelian differentials and various
mapping class groups afforded by means of the topological monodromy representation …

We propose a generalization of the concept of a ribbon graph suitable to provide
combinatorial models for marked surfaces equipped with a G-structure. Our main insight is …

The Arf-Brown invariant AB (Σ) is an 8th root of unity associated to a surface Σ equipped with
a Pin− structure. In this note we investigate a certain fully extended, invertible, topological …

For g≥ 5, we give a complete classification of the connected components of strata of abelian
differentials over Teichmüller space, establishing an analogue of Kontsevich and Zorich's …

We provide a combinatorial model for spin surfaces. Given a triangulation of an oriented
surface, a spin structure is encoded by assigning to each triangle a preferred edge, and to …

We show that for any surface of genus at least 3 equipped with any choice of framing, the
graph of non-separating curves with winding number 0 with respect to the framing is …